2 Answers
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The current scoring rules weren't decided on all at once. They evolved over the years.

At the outset, football was played according to whatever rules the two teams agreed to. The first rules meeting was in 1876. Before this, there was no standard ruleset for the sport of football.

Initially, it was the students at Rutgers, Princeton, Yale, and Harvard who created rules that varied from a strictly kicking game to a game that allowed running the ball.

The first ruleset, created in Princeton in 1871, included these rules related to scoring:

Games are played to to 4 of 7 goals (best of 7)

No player shall toss or carry the ball

Goalposts were 25 feet apart (kicking the ball through the goal posts was the only way to score)

Harvard drafted their own ruleset in 1872, based off of the Princeton/Rutgers rules. Theirs was closer to rugby, due to their Canadian connection with McGill University. Theirs allowed running and throwing:

No player may run with the ball unless pursued by an opponent, and only then so long as pursued

No player may pass or throw the ball unless pursued by an opponent

Scoring was still only by kicking through the goalposts

Yale created a ruleset very similar to Princeton's, prohibiting picking up, throwing, or carrying the ball.

In 1873, Princeton, Rutgers, and Yale met to organize a standard ruleset. The outcome was a set of 12 rules. Out of those, these related to scoring:

Games are to 6 goals. Goals are scored by the ball passing between the goal posts.

No player shall throw or carry the ball.

In 1876, Princeton, Yale, Columbia, and Harvard met to further unify the rulesets (Harvard had not attended the previous meeting due to their commitment to a running/Rugby style of game). The outcome was 61 rules. Here is how they related to scoring:

The rules defined punts, placekicks, and dropkicks

Goalposts now were based on top of a crossbar 10 feet from the ground

Goals are scored by any kick other than a punt that goes through the goalposts

Matches are decided on a majority of touchdowns (touchdowns had a different meaning than today)

A goal equals 4 touchdowns

A touchdown is when a player on the ball on the ground in touch or in goal so that the ball is dead

Players may run. If a player runs with the ball across the goal line and touches it down, it is called a run in.

Backward throws were allowed.

After a touchdown, the ball is brought out for an attempt at a goal (just like the extra point today)

In these rules, the safety was not explicitly stated but it was called a touch-in-goal. A team that has touched down the ball in their own goal were to immediately kick it away. These did not count against the team.

In 1881, the safety was officially included in the rules, and counted against the team, but only in a tie-break situation:

In case of a tie, [play more]. If the game still remains a tie, the side which makes four or more safeties less than their opponent shall win the game.

In 1882, safeties became part of the scoring, and the tie-break advantage switched from kicks to touchdowns:

Four touchdowns takes precedence over a goal from the field (which is worth four touchdowns)

Two safeties equals one touchdown

This was all part of an overall strategy to increase the pace of the game and eliminate stalling that occurred under the previous rules. Downs were also added at this time.

In early 1883, scores were first attached to the various ways of scoring:

Safety: 1 point

Touchdown: 2 points

Goal after touchdown: 4 points

Goal from the field: 5 points

Later in 1883, scores were further amended:

Safety: 2 points

Touchdown: 4 points

Goal after touchdown: 4 points

Goal from the field: 5 points

In 1887, scores became:

Safety: 2 points

Touchdown: 5 points

Goal after touchdown: 1 point

Goal from the field: 5 points

In 1904 and 1909, the goal from the field was reduced to 4, and then 3 points.

That is the history. It was never a decision involving the current scoring system versus something dramatically different. They were all incremental changes, being made to encourage certain types of play.

Note that football was an offshoot of rugby - therefore it was adopting a lot of the same rules rugby had. The two main differences in early football were the stoppages in play and downs.
– Coach-DNov 26 '18 at 5:24

The game evolved from Rugby Union, and at the time, the scoring just counted goals (similar to association football where this system is obviously still in place despite the rules of Rugby being officially 19-years older than soccer's (The Football Association) rules). Reaching the end zone merely gave you a chance to kick at the goal. Over time, both American football and rugby tweaked the scoring system to put more emphasis on reaching the end zone versus the kicking game.

The reason they arrived at these particular numbers was obviously just a long series of tweaking until the administrators arrived at a balance that they liked. For the same reason, numerous other rules are tweaked every year.